Railway Transition Curves Curvature—Should It Be Smooth in the Extreme Points or Not, or Something Else?

This work addresses the features of railway transition curves’ curvature, especially at extreme points. In particular, should it be smooth at the extreme points or not, or something else? Such a question is not accidental. This is based on the main results that the present authors obtained while optimizing the shape of polynomial railway transition curves. It appeared for the same quality function that, depending on the transition curve degree, the optimum shapes represented curvatures either possessing bends or close to smooth at the extreme points. Such a discrepancy raises the question of its reason, i.e., the factor influencing the appearance of bends at the extreme points of the curvatures the most. The continuity of G0 and G1 at such points was considered. At the same time, the hypothesis was formulated that a long time taken while negotiating the curve is the most influential factor of the existence of the mentioned bends in the extremities of curvature. Two cases were considered to ensure the long time of vehicle passage through the curve, with a great curve length and a small vehicle velocity, respectively. To verify the hypothesis, the optimizations of the shape of the transition curves of 5th, 9th, and 11th degrees and the simulations of the railway vehicle behaviour were performed. The hypothesis turned out to be true, although easier in application to long transition curves. It was shown that the transition curves’ shapes obtained in assumed circumstances did not have bends at the extreme points. The tendency to smoothen the curvature can be univocally noticed. It resulted in calmer vehicle movement, expressed by vehicle body lateral dynamical characteristics. Corresponding results of the simulations and transition curve optimizations were presented and compared.